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* Nikkei, Topix both rise 1 pct * Sharp falls on report of Apple cuts By Dominic Lau TOKYO, Jan 15 (Reuters) - Japan's Nikkei share average climbed 1 percent to a 32-month high on Tuesday, driving the benchmark further into "overbought" territory, as persistent weakness in the yen boosts demand for exporters' shares. The Nikkei rose 110.23 points to 10,911.80, setting its sights on the 11,000-mark, a level not seen since late April 2010. It rose 1.1 percent last week to log its ninth straight week of gains and its longest such winning run since 1988. Monday was a public holiday in Japan. Tuesday's bidding took the benchmark Nikkei deeper into "overbought" territory, with its 14-day relative strength index at 80.05, way above the 70-mark which is deemed overbought and often signals a near-term correction. "Short-term correction is getting more likely given that bullish sentiment ... has become more widespread. In terms of my positioning, I have trimmed down the exposure to stocks which have skyrocketed in the past two months," said Yasuo Sakuma, portfolio manager at Bayview Asset Management. The Nikkei has rallied 26 percent over the past two months, spurred by the weakness in the yen after Prime Minister Shinzo Abe called on the Bank of Japan to adopt aggressive policy to energise the ailing economy, including setting an inflation target of 2 percent. Exporters led the index higher on Tuesday, including Suzuki Motor Corp, Daikin Industries Ltd, Honda Motor Co, Olympus Corp and auto parts maker Denso Corp, which were up between 1.2 and 7.5 percent. Japanese automakers are aiming to shake off the lingering effects of natural disaster in 2011 and capitalise on the weakening yen and new products to increase sales in the United States, after a robust 2012. The yen was quoted at 89.55 to the dollar on Tuesday after falling 0.4 percent to a 2-1/2-year low of 89.67 yen in the previous session, while the Japanese currency was traded at 119.83 to the euro. Sharp Corp, however, sagged as much as 7 percent after the Nikkei newspaper said on Monday that Apple Inc has slashed orders with suppliers of LCD panels for the iPhone 5 in the current quarter due to weak demand. Other Apple suppliers in Japan also came under pressure, with Murata Manufacturing Co Ltd down 2.7 percent and Ibiden Co Ltd off 1.4 percent. The broader Topix gained 1 percent to 908.03. Japanese equities carry a 12-month forward price-to-earnings ratio of 13, ahead of the U.S. S&P 500's 12.9 and the pan-European STOXX Europe 600's 11.4, data from Thomson Reuters Datastream showed.